Even in hi-tech San Francisco, I spend roughly 2-3 hours of my work week without high speed internet access. (My provider, Comcast, has consistently crappy service, as evidenced by its recent third-to-last-place performance in a Harris Interactive poll of the reputations of major U.S. corporations, as described in the WSJ. On the bright side, Comcast did beat Halliburton, so I've got that going for me.)
Generally, I spend my time in forced offline purgatory doing things like berating the Comcast customer support person and trying to mooch limited connectivity from nearby wifi networks.
Until technology advances such that webpages, webmail and internal servers can be accessed offline—The Dojo Offline Toolkit will make this a possibility soon, says eWEEK—this frustration will continue. But there are plenty of productive things you can do on your computer even if you can't IM with colleagues or research a project on the web. You could, for example, try out some of these offline productivity ideas from Cleverclogs and Speaking Freely. My favorite tip from the latter site recommends deleting programs you don't use in order to speed up system scans, and, perhaps, your computer in general.